Proofiness: A look into how mathematics relates to American political life

Dearest readers,
This is my first post on The Virtuosi, so I thought I’d take a moment to
introduce myself. I’m a first year physics graduate student at Cornell,
recently joined after 2 years working as an engineer first at a private
firm and then at a national lab. I myself have had lots of fun following
the exploits of my estimable colleagues here on The Virtuosi, and I
thought I could bring a new angle to the content here. I would like to
use this space to discuss how science interacts with everyday life in a
cultural sense. How does science appear in popular culture? How do
political or social issues relate back to science? Those sorts of
questions. (I understand that there are plenty of other resources
elsewhere that offer far more intelligent insight into these matters
than I can, but in the very least this will give people a chance point
them out to me as they yell at me in the forum below.)
Enough intro, here begins my very first blog post:
Being interested in how science is communicated to the public, I am an
avid reader of popular science. While academic types sometimes dismiss
this kind of writing as shallow or otherwise uninteresting, I think
science writers perform a very important function serving as a way to
convey information about conceptually challenging topics to a general
audience. At their best, I find that these books serve as examples for
how I can communicate my own ideas better, and in addition challenge my
understanding of how science relates back to society in general.
This being said, I cannot recommend Charles Seife’s Proofiness enough.
The basic premise of this book is to explore the way that good
mathematics is hijacked, twisted, or ignored in everyday life, and the
ugly consequences of the tendency to misunderstand numbers and
measurements.
Seife gives a number of fascinating examples of the ways in which
numbers and math connect to American democracy. American government
functions through representation, and so the
“enumeration”
of citizens and their opinions through the Census and elections is an
essential part of the democratic process. This “enumeration” is a
counting measurement, subject to errors like any other. And yet, the
laws that govern how Censuses and elections are run ignore this fact.
Seife’s discussion of elections (and in particular Bush v. Gore) is
fascinating, but I won’t spoil that here. Here’s my take on the
discussion of the Census that appears in Proofiness:
Consider a (vague) physics experiment. I want to know how many particles
are inside a box. To figure this out, I have a detector that goes
ping every time a particle passes through it. I set up my detector
inside the box and count the number of times that it goes ping in a
certain amount of time. I can then use that count to guess at the number
of particles that I have in my box. My measurement will let me estimate
N to within some margin of error. This process is perhaps unnecessary if
I have only five particles in my box (in which case, I might just open
the box and count what I see inside), but if I have 300 million
particles in my box, it would be totally impractical for me to reach
into the box 300 million times and count each one individually.
We can consider the Census to be just like this physics experiment. I
have N inhabitants (particles) living in my country (box), and I can use
my detector (census replies) to count a certain number of people. In
principle, using well-understood statistical techniques of regression
and error analysis, I can estimate to within a very good margin of error
how many people live in each region of the country. Instead, what the
Census requires is that we reach inside the box (send representatives to
every household that doesn’t reply by mail) and count every single
person. The whole process ignores the fact that even if we send a
representative to every single household there will still be some margin
of error in our counting measurements. No such measurement can be made
without errors.
The consequences of ignoring these errors, says Seife, can be that we
waste money in attempting the impossible and trying to count everybody.
From a civic-minded perspective, this attitude towards the perfection of
the Census can backfire. For example, if undercounting occurs (i.e.,
certain households do not respond for some reason), the Census has no
mechanism for correcting that miscount. Counter-intuitively, the Census
laws actually prohibit the use of any statistical techniques to correct
miscounting. The result is that those slow to respond are ignored and
not taken into account when allotting seats in the legislature to
represent them.
Proofiness is a fascinating book and a fun read, and I recommend you
all look it up. In addition, it serves as an excellent example of
science writing that helped me to rethink how scientific ideas relate to
everyday life. I hope to invite consideration of these topics here and
in future posts. If you want to know more about the inspiration for this
post, go here.